We are interested in generalizations of the concepts of t-norm and t-conorm. In a companion chapter in this volume [14] we have presented a family of hypert-norms ∧q and a family of hyper-t-conorms ∨p. The prefix hyper is used to indicate multi-valued operations, also known as hyperoperations (see [5, 14]), i.e. operations which map pairs of elements to sets of elements. See [14] for the constr...

In this paper we start with a lattice (X,∨,∧) and define, in terms of ∨, a family of crisp hyperoperations tp (one hyperoperation for each p ∈ X). We show that, for every p, the hyperalgebra (X,tp) is a join space and the hyperalgebra (X,tp,∧) is very similar to a hyperlattice. Then we use the hyperoperations tp as p-cuts to introduce an L-fuzzy hyperoperation t and show that (X,t) is an L-fuzz...

In this paper we study the L-fuzzy hyperoperation t, which generalizes the crisp Nakano hyperoperation t1. We construct t using a family of crisp tp hyperoperations as its p-cuts. The hyperalgebra (X,t,∧) can be understood as an L-fuzzy hyperlattice. AMS Classification: 06B99, 06D30, 08A72, 03E72, 20N20.

Hyperstructures and binary relations have been studied by many researchers, for instance, Chvalina 1, 2 , Corsini and Leoreanu 3 , Feng 4 , Hort 5 , Rosenberg 6 , Spartalis 7 , and so on. A partial hypergroupoid 〈H, ∗〉 is a nonempty setH with a function fromH×H to the set of subsets of H. A hypergroupoid is a nonempty set H, endowed with a hyperoperation, that is, a function fromH ×H to P H , t...

the operations in the set of fuzzy numbers are usually obtained bythe zadeh extension principle. but these definitions can have some disadvantagesfor the applications both by an algebraic point of view and by practicalaspects. in fact the zadeh multiplication is not distributive with respect tothe addition, the shape of fuzzy numbers is not preserved by multiplication,the indeterminateness of t...

On a hypergroupoid one can define a topology such that the hyperoperationis pseudocontinuous or continuous. In this paper we extend thisconcepts to the fuzzy case. We give a connection between the classical and thefuzzy (pseudo)continuous hyperoperations.

on a hypergroupoid one can define a topology such that the hyperoperationis pseudocontinuous or continuous. in this paper we extend thisconcepts to the fuzzy case. we give a connection between the classical and thefuzzy (pseudo)continuous hyperoperations.

In the set N of the Natural Numbers we define two hyperoperations based on the divisors of the addition and multiplication of two numbers. Then, the properties of these two hyperoperations are studied together with the resulting hyperstructures. Furthermore, from the coexistence of these two hyperoperations in N∗, an Hv-ring is resulting which is dual.

In this paper, we extend the notion of semi-hypergroups (resp. hypergroups) to neutro-semihypergroups neutro-hypergroups). We investigate property anti-semihypergroups anti-hypergroups). also give a new alternative neutro-hyperoperations anti-hyperoperations), neutro-hyperoperation-sophications anti-hypersophications). Moreover, show that these concepts are different from classical by several e...

Hypergroups are generalizations of groups. If this binary operation is taken to be multivalued, then we arrive at a hypergroup. The motivation for generalization of the notion of group resulted naturally from various problems in non-commutative algebra, another motivation for such an investigation came from geometry. In various branches of mathematics we encounter important examples of topologi...